Transversely Isotropic Composites with Statistically Oriented Inclusions
Salvatore Federico (The University of Calgary), Alfio Grillo (Polytechnic of Torino), Walter Herzog (The University of Calgary)
Prager Medal Symposium in honor of George Weng: Micromechanics, Composites and Multifunctional Materials
Mon 4:20 - 5:40
MacMillan 117
In the literature, the determination of the global elastic properties of composites with ellipsoidal inclusions is based on the averaged stress, strain and elastic-energy fields, which are related to the local fields of the inclusion, the matrix, and the inclusion-matrix interface (e.g., Mori and Tanaka, 1973; Tandon and Weng, 1986; Qiu and Weng, 1990). We have addressed the problem of obtaining the elasticity tensor of any transversely isotropic composite directly from the elasticity tensors of the matrix and the inclusions (Federico et al., 2004), without referring to the stress and strain fields applied globally or generated locally. The problem is entirely geometrized and any arbitrary transversely isotropic probability distribution of orientation of the inclusions is treated in terms of directional averages of Walpole’s (1981) components of the fourth-order tensors describing the problem. We give a general numerical solution for any transversely isotropic statistical distribution of orientation, and also provide a validation of our method by applying it to some known cases and by retrieving the known exact solutions from the literature. Since its development, this work has served as the basic framework from which a family of models of fibre-reinforced materials arose, including non-linear elasticity, as well as the case of a fluid-saturated permeable matrix reinforced by impermeable fibres, both under small and large deformations. These models have found wide applications in the study of hydrated soft biological tissues, such as articular cartilage. References Federico, S., Grillo, A., Herzog, W., 2004, J. Mech. Phys. Solids 52, 2309-2327 Mori, T., Tanaka, K., 1973, Acta Metall. 21, 571-574. Qiu, Y.P., Weng, G.J., 1990, Int. J. Eng. Sci. 28, 1121-1137. Tandon, G.P., Weng, G.J., 1986, Compos. Sci. Technol. 27, 111-132. Walpole, L.J., 1981, Adv. Appl. Mech. 21, 169-242.